Question

factor completely.
27t³ + 18t² + 30t + 20

Explanation:

Step1: Group the terms

Group the first two terms and the last two terms:
$(27t^3 + 18t^2) + (30t + 20)$

Step2: Factor out GCF from each group

Factor out $9t^2$ from the first group and $10$ from the second group:
$9t^2(3t + 2) + 10(3t + 2)$

Step3: Factor out the common binomial factor

Now, factor out the common binomial factor $(3t + 2)$:
$(3t + 2)(9t^2 + 10)$

Answer:

$(3t + 2)(9t^2 + 10)$